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<article id="content">
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<header>
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<h1 class="title">Module <code>miplearn.problems.tsp</code></h1>
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</header>
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<section id="section-intro">
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<details class="source">
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<summary>
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<span>Expand source code</span>
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</summary>
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<pre><code class="python"># MIPLearn: Extensible Framework for Learning-Enhanced Mixed-Integer Optimization
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# Copyright (C) 2020, UChicago Argonne, LLC. All rights reserved.
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# Released under the modified BSD license. See COPYING.md for more details.
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import networkx as nx
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import numpy as np
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import pyomo.environ as pe
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from scipy.spatial.distance import pdist, squareform
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from scipy.stats import uniform, randint
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from scipy.stats.distributions import rv_frozen
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from miplearn.instance import Instance
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class ChallengeA:
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def __init__(
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self,
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seed=42,
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n_training_instances=500,
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n_test_instances=50,
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):
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np.random.seed(seed)
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self.generator = TravelingSalesmanGenerator(
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x=uniform(loc=0.0, scale=1000.0),
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y=uniform(loc=0.0, scale=1000.0),
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n=randint(low=350, high=351),
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gamma=uniform(loc=0.95, scale=0.1),
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fix_cities=True,
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round=True,
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)
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np.random.seed(seed + 1)
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self.training_instances = self.generator.generate(n_training_instances)
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np.random.seed(seed + 2)
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self.test_instances = self.generator.generate(n_test_instances)
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class TravelingSalesmanGenerator:
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"""Random generator for the Traveling Salesman Problem."""
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def __init__(
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self,
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x=uniform(loc=0.0, scale=1000.0),
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y=uniform(loc=0.0, scale=1000.0),
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n=randint(low=100, high=101),
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gamma=uniform(loc=1.0, scale=0.0),
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fix_cities=True,
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round=True,
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):
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"""Initializes the problem generator.
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Initially, the generator creates n cities (x_1,y_1),...,(x_n,y_n) where n, x_i and y_i are
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sampled independently from the provided probability distributions `n`, `x` and `y`. For each
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(unordered) pair of cities (i,j), the distance d[i,j] between them is set to:
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d[i,j] = gamma[i,j] \sqrt{(x_i - x_j)^2 + (y_i - y_j)^2}
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where gamma is sampled from the provided probability distribution `gamma`.
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If fix_cities=True, the list of cities is kept the same for all generated instances. The
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gamma values, and therefore also the distances, are still different.
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By default, all distances d[i,j] are rounded to the nearest integer. If `round=False`
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is provided, this rounding will be disabled.
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Arguments
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---------
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x: rv_continuous
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Probability distribution for the x-coordinate of each city.
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y: rv_continuous
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Probability distribution for the y-coordinate of each city.
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n: rv_discrete
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Probability distribution for the number of cities.
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fix_cities: bool
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If False, cities will be resampled for every generated instance. Otherwise, list of
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cities will be computed once, during the constructor.
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round: bool
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If True, distances are rounded to the nearest integer.
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"""
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assert isinstance(x, rv_frozen), "x should be a SciPy probability distribution"
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assert isinstance(y, rv_frozen), "y should be a SciPy probability distribution"
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assert isinstance(n, rv_frozen), "n should be a SciPy probability distribution"
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assert isinstance(
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gamma,
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rv_frozen,
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), "gamma should be a SciPy probability distribution"
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self.x = x
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self.y = y
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self.n = n
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self.gamma = gamma
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self.round = round
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if fix_cities:
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self.fixed_n, self.fixed_cities = self._generate_cities()
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else:
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self.fixed_n = None
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self.fixed_cities = None
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def generate(self, n_samples):
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def _sample():
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if self.fixed_cities is not None:
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n, cities = self.fixed_n, self.fixed_cities
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else:
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n, cities = self._generate_cities()
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distances = squareform(pdist(cities)) * self.gamma.rvs(size=(n, n))
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distances = np.tril(distances) + np.triu(distances.T, 1)
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if self.round:
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distances = distances.round()
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return TravelingSalesmanInstance(n, distances)
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return [_sample() for _ in range(n_samples)]
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def _generate_cities(self):
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n = self.n.rvs()
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cities = np.array([(self.x.rvs(), self.y.rvs()) for _ in range(n)])
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return n, cities
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class TravelingSalesmanInstance(Instance):
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"""An instance ot the Traveling Salesman Problem.
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Given a list of cities and the distance between each pair of cities, the problem asks for the
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shortest route starting at the first city, visiting each other city exactly once, then
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returning to the first city. This problem is a generalization of the Hamiltonian path problem,
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one of Karp's 21 NP-complete problems.
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"""
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def __init__(self, n_cities, distances):
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assert isinstance(distances, np.ndarray)
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assert distances.shape == (n_cities, n_cities)
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self.n_cities = n_cities
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self.distances = distances
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def to_model(self):
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model = pe.ConcreteModel()
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model.edges = edges = [
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(i, j) for i in range(self.n_cities) for j in range(i + 1, self.n_cities)
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]
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model.x = pe.Var(edges, domain=pe.Binary)
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model.obj = pe.Objective(
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expr=sum(model.x[i, j] * self.distances[i, j] for (i, j) in edges),
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sense=pe.minimize,
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)
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model.eq_degree = pe.ConstraintList()
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model.eq_subtour = pe.ConstraintList()
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for i in range(self.n_cities):
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model.eq_degree.add(
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sum(
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model.x[min(i, j), max(i, j)]
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for j in range(self.n_cities)
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if i != j
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)
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== 2
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)
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return model
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def get_instance_features(self):
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return np.array([1])
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def get_variable_features(self, var_name, index):
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return np.array([1])
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def get_variable_category(self, var_name, index):
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return index
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def find_violated_lazy_constraints(self, model):
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selected_edges = [e for e in model.edges if model.x[e].value > 0.5]
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graph = nx.Graph()
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graph.add_edges_from(selected_edges)
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components = [frozenset(c) for c in list(nx.connected_components(graph))]
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violations = []
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for c in components:
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if len(c) < self.n_cities:
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violations += [c]
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return violations
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def build_lazy_constraint(self, model, component):
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cut_edges = [
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e
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for e in model.edges
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if (e[0] in component and e[1] not in component)
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or (e[0] not in component and e[1] in component)
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]
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return model.eq_subtour.add(sum(model.x[e] for e in cut_edges) >= 2)
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def find_violated_user_cuts(self, model):
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return self.find_violated_lazy_constraints(model)
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def build_user_cut(self, model, violation):
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return self.build_lazy_constraint(model, violation)</code></pre>
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</details>
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</section>
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<section>
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</section>
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<section>
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</section>
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<section>
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</section>
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<section>
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<h2 class="section-title" id="header-classes">Classes</h2>
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<dl>
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<dt id="miplearn.problems.tsp.ChallengeA"><code class="flex name class">
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<span>class <span class="ident">ChallengeA</span></span>
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<span>(</span><span>seed=42, n_training_instances=500, n_test_instances=50)</span>
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</code></dt>
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<dd>
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<section class="desc"></section>
|
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<details class="source">
|
|
<summary>
|
|
<span>Expand source code</span>
|
|
</summary>
|
|
<pre><code class="python">class ChallengeA:
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|
def __init__(
|
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self,
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|
seed=42,
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n_training_instances=500,
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|
n_test_instances=50,
|
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):
|
|
|
|
np.random.seed(seed)
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self.generator = TravelingSalesmanGenerator(
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x=uniform(loc=0.0, scale=1000.0),
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y=uniform(loc=0.0, scale=1000.0),
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n=randint(low=350, high=351),
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gamma=uniform(loc=0.95, scale=0.1),
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fix_cities=True,
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round=True,
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)
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np.random.seed(seed + 1)
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self.training_instances = self.generator.generate(n_training_instances)
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np.random.seed(seed + 2)
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self.test_instances = self.generator.generate(n_test_instances)</code></pre>
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</details>
|
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</dd>
|
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<dt id="miplearn.problems.tsp.TravelingSalesmanGenerator"><code class="flex name class">
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<span>class <span class="ident">TravelingSalesmanGenerator</span></span>
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<span>(</span><span>x=<scipy.stats._distn_infrastructure.rv_frozen object>, y=<scipy.stats._distn_infrastructure.rv_frozen object>, n=<scipy.stats._distn_infrastructure.rv_frozen object>, gamma=<scipy.stats._distn_infrastructure.rv_frozen object>, fix_cities=True, round=True)</span>
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</code></dt>
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<dd>
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<section class="desc"><p>Random generator for the Traveling Salesman Problem.</p>
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<p>Initializes the problem generator.</p>
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<p>Initially, the generator creates n cities (x_1,y_1),…,(x_n,y_n) where n, x_i and y_i are
|
|
sampled independently from the provided probability distributions <code>n</code>, <code>x</code> and <code>y</code>. For each
|
|
(unordered) pair of cities (i,j), the distance d[i,j] between them is set to:</p>
|
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<pre><code>d[i,j] = gamma[i,j] \sqrt{(x_i - x_j)^2 + (y_i - y_j)^2}
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|
</code></pre>
|
|
<p>where gamma is sampled from the provided probability distribution <code>gamma</code>.</p>
|
|
<p>If fix_cities=True, the list of cities is kept the same for all generated instances. The
|
|
gamma values, and therefore also the distances, are still different.</p>
|
|
<p>By default, all distances d[i,j] are rounded to the nearest integer.
|
|
If <code>round=False</code>
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is provided, this rounding will be disabled.</p>
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<h2 id="arguments">Arguments</h2>
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<dl>
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<dt><strong><code>x</code></strong> : <code>rv_continuous</code></dt>
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<dd>Probability distribution for the x-coordinate of each city.</dd>
|
|
<dt><strong><code>y</code></strong> : <code>rv_continuous</code></dt>
|
|
<dd>Probability distribution for the y-coordinate of each city.</dd>
|
|
<dt><strong><code>n</code></strong> : <code>rv_discrete</code></dt>
|
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<dd>Probability distribution for the number of cities.</dd>
|
|
<dt><strong><code>fix_cities</code></strong> : <code>bool</code></dt>
|
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<dd>If False, cities will be resampled for every generated instance. Otherwise, list of
|
|
cities will be computed once, during the constructor.</dd>
|
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<dt><strong><code>round</code></strong> : <code>bool</code></dt>
|
|
<dd>If True, distances are rounded to the nearest integer.</dd>
|
|
</dl></section>
|
|
<details class="source">
|
|
<summary>
|
|
<span>Expand source code</span>
|
|
</summary>
|
|
<pre><code class="python">class TravelingSalesmanGenerator:
|
|
"""Random generator for the Traveling Salesman Problem."""
|
|
|
|
def __init__(
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self,
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|
x=uniform(loc=0.0, scale=1000.0),
|
|
y=uniform(loc=0.0, scale=1000.0),
|
|
n=randint(low=100, high=101),
|
|
gamma=uniform(loc=1.0, scale=0.0),
|
|
fix_cities=True,
|
|
round=True,
|
|
):
|
|
"""Initializes the problem generator.
|
|
|
|
Initially, the generator creates n cities (x_1,y_1),...,(x_n,y_n) where n, x_i and y_i are
|
|
sampled independently from the provided probability distributions `n`, `x` and `y`. For each
|
|
(unordered) pair of cities (i,j), the distance d[i,j] between them is set to:
|
|
|
|
d[i,j] = gamma[i,j] \sqrt{(x_i - x_j)^2 + (y_i - y_j)^2}
|
|
|
|
where gamma is sampled from the provided probability distribution `gamma`.
|
|
|
|
If fix_cities=True, the list of cities is kept the same for all generated instances. The
|
|
gamma values, and therefore also the distances, are still different.
|
|
|
|
By default, all distances d[i,j] are rounded to the nearest integer. If `round=False`
|
|
is provided, this rounding will be disabled.
|
|
|
|
Arguments
|
|
---------
|
|
x: rv_continuous
|
|
Probability distribution for the x-coordinate of each city.
|
|
y: rv_continuous
|
|
Probability distribution for the y-coordinate of each city.
|
|
n: rv_discrete
|
|
Probability distribution for the number of cities.
|
|
fix_cities: bool
|
|
If False, cities will be resampled for every generated instance. Otherwise, list of
|
|
cities will be computed once, during the constructor.
|
|
round: bool
|
|
If True, distances are rounded to the nearest integer.
|
|
"""
|
|
assert isinstance(x, rv_frozen), "x should be a SciPy probability distribution"
|
|
assert isinstance(y, rv_frozen), "y should be a SciPy probability distribution"
|
|
assert isinstance(n, rv_frozen), "n should be a SciPy probability distribution"
|
|
assert isinstance(
|
|
gamma,
|
|
rv_frozen,
|
|
), "gamma should be a SciPy probability distribution"
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self.x = x
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self.y = y
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self.n = n
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self.gamma = gamma
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self.round = round
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|
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if fix_cities:
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self.fixed_n, self.fixed_cities = self._generate_cities()
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else:
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self.fixed_n = None
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self.fixed_cities = None
|
|
|
|
def generate(self, n_samples):
|
|
def _sample():
|
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if self.fixed_cities is not None:
|
|
n, cities = self.fixed_n, self.fixed_cities
|
|
else:
|
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n, cities = self._generate_cities()
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distances = squareform(pdist(cities)) * self.gamma.rvs(size=(n, n))
|
|
distances = np.tril(distances) + np.triu(distances.T, 1)
|
|
if self.round:
|
|
distances = distances.round()
|
|
return TravelingSalesmanInstance(n, distances)
|
|
|
|
return [_sample() for _ in range(n_samples)]
|
|
|
|
def _generate_cities(self):
|
|
n = self.n.rvs()
|
|
cities = np.array([(self.x.rvs(), self.y.rvs()) for _ in range(n)])
|
|
return n, cities</code></pre>
|
|
</details>
|
|
<h3>Methods</h3>
|
|
<dl>
|
|
<dt id="miplearn.problems.tsp.TravelingSalesmanGenerator.generate"><code class="name flex">
|
|
<span>def <span class="ident">generate</span></span>(<span>self, n_samples)</span>
|
|
</code></dt>
|
|
<dd>
|
|
<section class="desc"></section>
|
|
<details class="source">
|
|
<summary>
|
|
<span>Expand source code</span>
|
|
</summary>
|
|
<pre><code class="python">def generate(self, n_samples):
|
|
def _sample():
|
|
if self.fixed_cities is not None:
|
|
n, cities = self.fixed_n, self.fixed_cities
|
|
else:
|
|
n, cities = self._generate_cities()
|
|
distances = squareform(pdist(cities)) * self.gamma.rvs(size=(n, n))
|
|
distances = np.tril(distances) + np.triu(distances.T, 1)
|
|
if self.round:
|
|
distances = distances.round()
|
|
return TravelingSalesmanInstance(n, distances)
|
|
|
|
return [_sample() for _ in range(n_samples)]</code></pre>
|
|
</details>
|
|
</dd>
|
|
</dl>
|
|
</dd>
|
|
<dt id="miplearn.problems.tsp.TravelingSalesmanInstance"><code class="flex name class">
|
|
<span>class <span class="ident">TravelingSalesmanInstance</span></span>
|
|
<span>(</span><span>n_cities, distances)</span>
|
|
</code></dt>
|
|
<dd>
|
|
<section class="desc"><p>An instance ot the Traveling Salesman Problem.</p>
|
|
<p>Given a list of cities and the distance between each pair of cities, the problem asks for the
|
|
shortest route starting at the first city, visiting each other city exactly once, then
|
|
returning to the first city. This problem is a generalization of the Hamiltonian path problem,
|
|
one of Karp's 21 NP-complete problems.</p></section>
|
|
<details class="source">
|
|
<summary>
|
|
<span>Expand source code</span>
|
|
</summary>
|
|
<pre><code class="python">class TravelingSalesmanInstance(Instance):
|
|
"""An instance ot the Traveling Salesman Problem.
|
|
|
|
Given a list of cities and the distance between each pair of cities, the problem asks for the
|
|
shortest route starting at the first city, visiting each other city exactly once, then
|
|
returning to the first city. This problem is a generalization of the Hamiltonian path problem,
|
|
one of Karp's 21 NP-complete problems.
|
|
"""
|
|
|
|
def __init__(self, n_cities, distances):
|
|
assert isinstance(distances, np.ndarray)
|
|
assert distances.shape == (n_cities, n_cities)
|
|
self.n_cities = n_cities
|
|
self.distances = distances
|
|
|
|
def to_model(self):
|
|
model = pe.ConcreteModel()
|
|
model.edges = edges = [
|
|
(i, j) for i in range(self.n_cities) for j in range(i + 1, self.n_cities)
|
|
]
|
|
model.x = pe.Var(edges, domain=pe.Binary)
|
|
model.obj = pe.Objective(
|
|
expr=sum(model.x[i, j] * self.distances[i, j] for (i, j) in edges),
|
|
sense=pe.minimize,
|
|
)
|
|
model.eq_degree = pe.ConstraintList()
|
|
model.eq_subtour = pe.ConstraintList()
|
|
for i in range(self.n_cities):
|
|
model.eq_degree.add(
|
|
sum(
|
|
model.x[min(i, j), max(i, j)]
|
|
for j in range(self.n_cities)
|
|
if i != j
|
|
)
|
|
== 2
|
|
)
|
|
return model
|
|
|
|
def get_instance_features(self):
|
|
return np.array([1])
|
|
|
|
def get_variable_features(self, var_name, index):
|
|
return np.array([1])
|
|
|
|
def get_variable_category(self, var_name, index):
|
|
return index
|
|
|
|
def find_violated_lazy_constraints(self, model):
|
|
selected_edges = [e for e in model.edges if model.x[e].value > 0.5]
|
|
graph = nx.Graph()
|
|
graph.add_edges_from(selected_edges)
|
|
components = [frozenset(c) for c in list(nx.connected_components(graph))]
|
|
violations = []
|
|
for c in components:
|
|
if len(c) < self.n_cities:
|
|
violations += [c]
|
|
return violations
|
|
|
|
def build_lazy_constraint(self, model, component):
|
|
cut_edges = [
|
|
e
|
|
for e in model.edges
|
|
if (e[0] in component and e[1] not in component)
|
|
or (e[0] not in component and e[1] in component)
|
|
]
|
|
return model.eq_subtour.add(sum(model.x[e] for e in cut_edges) >= 2)
|
|
|
|
def find_violated_user_cuts(self, model):
|
|
return self.find_violated_lazy_constraints(model)
|
|
|
|
def build_user_cut(self, model, violation):
|
|
return self.build_lazy_constraint(model, violation)</code></pre>
|
|
</details>
|
|
<h3>Ancestors</h3>
|
|
<ul class="hlist">
|
|
<li><a title="miplearn.instance.Instance" href="../instance.html#miplearn.instance.Instance">Instance</a></li>
|
|
<li>abc.ABC</li>
|
|
</ul>
|
|
<h3>Methods</h3>
|
|
<dl>
|
|
<dt id="miplearn.problems.tsp.TravelingSalesmanInstance.build_user_cut"><code class="name flex">
|
|
<span>def <span class="ident">build_user_cut</span></span>(<span>self, model, violation)</span>
|
|
</code></dt>
|
|
<dd>
|
|
<section class="desc"></section>
|
|
<details class="source">
|
|
<summary>
|
|
<span>Expand source code</span>
|
|
</summary>
|
|
<pre><code class="python">def build_user_cut(self, model, violation):
|
|
return self.build_lazy_constraint(model, violation)</code></pre>
|
|
</details>
|
|
</dd>
|
|
<dt id="miplearn.problems.tsp.TravelingSalesmanInstance.find_violated_user_cuts"><code class="name flex">
|
|
<span>def <span class="ident">find_violated_user_cuts</span></span>(<span>self, model)</span>
|
|
</code></dt>
|
|
<dd>
|
|
<section class="desc"></section>
|
|
<details class="source">
|
|
<summary>
|
|
<span>Expand source code</span>
|
|
</summary>
|
|
<pre><code class="python">def find_violated_user_cuts(self, model):
|
|
return self.find_violated_lazy_constraints(model)</code></pre>
|
|
</details>
|
|
</dd>
|
|
</dl>
|
|
<h3>Inherited members</h3>
|
|
<ul class="hlist">
|
|
<li><code><b><a title="miplearn.instance.Instance" href="../instance.html#miplearn.instance.Instance">Instance</a></b></code>:
|
|
<ul class="hlist">
|
|
<li><code><a title="miplearn.instance.Instance.build_lazy_constraint" href="../instance.html#miplearn.instance.Instance.build_lazy_constraint">build_lazy_constraint</a></code></li>
|
|
<li><code><a title="miplearn.instance.Instance.find_violated_lazy_constraints" href="../instance.html#miplearn.instance.Instance.find_violated_lazy_constraints">find_violated_lazy_constraints</a></code></li>
|
|
<li><code><a title="miplearn.instance.Instance.get_instance_features" href="../instance.html#miplearn.instance.Instance.get_instance_features">get_instance_features</a></code></li>
|
|
<li><code><a title="miplearn.instance.Instance.get_variable_category" href="../instance.html#miplearn.instance.Instance.get_variable_category">get_variable_category</a></code></li>
|
|
<li><code><a title="miplearn.instance.Instance.get_variable_features" href="../instance.html#miplearn.instance.Instance.get_variable_features">get_variable_features</a></code></li>
|
|
<li><code><a title="miplearn.instance.Instance.to_model" href="../instance.html#miplearn.instance.Instance.to_model">to_model</a></code></li>
|
|
</ul>
|
|
</li>
|
|
</ul>
|
|
</dd>
|
|
</dl>
|
|
</section>
|
|
</article>
|
|
<nav id="sidebar">
|
|
<h1>Index</h1>
|
|
<div class="toc">
|
|
<ul></ul>
|
|
</div>
|
|
<ul id="index">
|
|
<li><h3>Super-module</h3>
|
|
<ul>
|
|
<li><code><a title="miplearn.problems" href="index.html">miplearn.problems</a></code></li>
|
|
</ul>
|
|
</li>
|
|
<li><h3><a href="#header-classes">Classes</a></h3>
|
|
<ul>
|
|
<li>
|
|
<h4><code><a title="miplearn.problems.tsp.ChallengeA" href="#miplearn.problems.tsp.ChallengeA">ChallengeA</a></code></h4>
|
|
</li>
|
|
<li>
|
|
<h4><code><a title="miplearn.problems.tsp.TravelingSalesmanGenerator" href="#miplearn.problems.tsp.TravelingSalesmanGenerator">TravelingSalesmanGenerator</a></code></h4>
|
|
<ul class="">
|
|
<li><code><a title="miplearn.problems.tsp.TravelingSalesmanGenerator.generate" href="#miplearn.problems.tsp.TravelingSalesmanGenerator.generate">generate</a></code></li>
|
|
</ul>
|
|
</li>
|
|
<li>
|
|
<h4><code><a title="miplearn.problems.tsp.TravelingSalesmanInstance" href="#miplearn.problems.tsp.TravelingSalesmanInstance">TravelingSalesmanInstance</a></code></h4>
|
|
<ul class="">
|
|
<li><code><a title="miplearn.problems.tsp.TravelingSalesmanInstance.build_user_cut" href="#miplearn.problems.tsp.TravelingSalesmanInstance.build_user_cut">build_user_cut</a></code></li>
|
|
<li><code><a title="miplearn.problems.tsp.TravelingSalesmanInstance.find_violated_user_cuts" href="#miplearn.problems.tsp.TravelingSalesmanInstance.find_violated_user_cuts">find_violated_user_cuts</a></code></li>
|
|
</ul>
|
|
</li>
|
|
</ul>
|
|
</li>
|
|
</ul>
|
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</nav>
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